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Abstract:
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We propose a partially-global Fréchet regression model by extending the profiling technique for the partially linear regression model (Severini and Wong 1992). This extension allows for the response to come from a generic metric space and can further incorporate predictors from another generic metric space, scalar predictors, or combinations of the two. By melding together the local and global Fréchet regression models proposed by Petersen and Müller (2019), we gain a model that is more flexible than global Fréchet regression and more accurate than local Fréchet regression when the data generating process is truly "global (linear)" for some scalar predictors or relies on non-Euclidean predictors. In this paper, we provide theoretical support for partially-global Fréchet regression and demonstrate its competitive finite-sample performance when applied to both simulated data and to real data which is too complex for traditional statistical methods.
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